An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms
An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equations in time fractional forms. Compatible fractional traveling wave transform plays a key role to b...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Sociedade Brasileira de Matemática
2022-01-01
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| Series: | Boletim da Sociedade Paranaense de Matemática |
| Online Access: | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/44592 |
| _version_ | 1827767254868033536 |
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| author | Ozlem Ersoy Hepson Alper Korkmaz Kamyar Hosseini Hadi Rezazadeh Mostafa Eslami |
| author_facet | Ozlem Ersoy Hepson Alper Korkmaz Kamyar Hosseini Hadi Rezazadeh Mostafa Eslami |
| author_sort | Ozlem Ersoy Hepson |
| collection | DOAJ |
| description |
An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equations in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions. Some exact solutions in traveling wave forms are explicitly expressed by the proposed method for both the Korteweg-de Vries and modified Korteweg-de Vries equations.
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| first_indexed | 2024-03-11T11:55:10Z |
| format | Article |
| id | doaj.art-d062556437a54d4a87a60f2378cb8829 |
| institution | Directory Open Access Journal |
| issn | 0037-8712 2175-1188 |
| language | English |
| last_indexed | 2024-03-11T11:55:10Z |
| publishDate | 2022-01-01 |
| publisher | Sociedade Brasileira de Matemática |
| record_format | Article |
| series | Boletim da Sociedade Paranaense de Matemática |
| spelling | doaj.art-d062556437a54d4a87a60f2378cb88292023-11-08T19:49:41ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882022-01-014010.5269/bspm.44592An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional formsOzlem Ersoy Hepson0Alper Korkmaz1Kamyar Hosseini2Hadi Rezazadeh3Mostafa Eslami4ESOGUÇAKUAhrar Institute of Technology and Higher EducationAmol University of Special Modern TechnologiesUniversity of Mazandaran An expansion method based on time fractional Sine-Gordon equation is implemented to construct some real and complex valued exact solutions to the Korteweg-de Vries and modified Korteweg-de Vries equations in time fractional forms. Compatible fractional traveling wave transform plays a key role to be able to apply homogeneous balance technique to set the predicted solution. The relation between trigonometric and hyperbolic functions based on fractional Sine-Gordon equation allows to form the exact solutions with multiplication of powers of hyperbolic functions. Some exact solutions in traveling wave forms are explicitly expressed by the proposed method for both the Korteweg-de Vries and modified Korteweg-de Vries equations. https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/44592 |
| spellingShingle | Ozlem Ersoy Hepson Alper Korkmaz Kamyar Hosseini Hadi Rezazadeh Mostafa Eslami An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms Boletim da Sociedade Paranaense de Matemática |
| title | An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms |
| title_full | An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms |
| title_fullStr | An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms |
| title_full_unstemmed | An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms |
| title_short | An expansion based on Sine-Gordon equation to Solve KdV and modified KdV equations in conformable fractional forms |
| title_sort | expansion based on sine gordon equation to solve kdv and modified kdv equations in conformable fractional forms |
| url | https://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/44592 |
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